Predictive Uncertainty Estimation of Hydrological Multi-Model Ensembles Using Pair-Copula Construction

Bastian Klein,Dennis Meissner,Hans-Ulrich Kobialka,Paolo Reggiani

doi:10.3390/w8040125

Abstract

Predictive uncertainty (PU) is defined as the probability of occurrence of an observed variable of interest, conditional on all available information. In this context, hydrological model predictions and forecasts are considered to be accessible but yet uncertain information. To estimate the PU of hydrological multi-model ensembles, we apply a method based on the use of copulas which enables modelling the dependency structures between variates independently of their marginal distributions. Given that the option to employ copula functions imposes certain limitations in the multivariate case, we model the multivariate distribution as a cascade of bivariate copulas by using the pair-copula construction. We apply a mixture of probability distributions to estimate the marginal densities and distributions of daily flow rates for various meteorological and hydrological situations. The proposed method is applied to a multi-model ensemble involving two hydrological and one statistical flow models at two gauge stations in the Moselle river basin. Verification and inter-comparison with other PU assessment methods show that copulas are well-suited for this scope and constitute a valid approach for predictive uncertainty estimation of hydrological multi-model predictions.

Highlights

Hydrological real-time forecasts are important means for decision support in water resources management and optimal control of rivers, for instance, for navigation or hydropower production.At the same time, forecasts are invaluable for flood risk management, as demonstrated during the major floods in Central Europe in June 2013
The observed and simulated values y are first transformed to the Normal variable η and the estimated quantiles of the predictive uncertainty are back-transformed to the real space by the inverse transform
To ensure that no flow values are simultaneously used for parameter estimation and validation of the predictive distribution, we used a Leave-One-Out Cross Validation (LOOCV) procedure

Summary

Introduction

Hydrological real-time forecasts are important means for decision support in water resources management and optimal control of rivers, for instance, for navigation or hydropower production. Forecasts are invaluable for flood risk management, as demonstrated during the major floods in Central Europe in June 2013. The benefit of an operational forecasting system depends foremost on the reliability and accuracy of the hydrological prediction. Excess non-quantified uncertainty reduces the benefits of predictions in the decision-making process. Sources of uncertainty in the meteorological-hydrological forecasting chain are attributable to meteorological observations (i.e., measurement and interpolation errors) and numerical weather forecasts (chaotic-deterministic behavior of atmospheric processes), model errors and parameter uncertainty as well as knowledge gaps on initial and boundary conditions of hydrological and hydraulic models used for flow prediction.

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Conclusion